X is the midpoint of UV. Y is the midpoint of UW. If m∠UXY = 58, find m∠V.

∠UXY and ∠V are corresponding angles, therefore m∠V = 58°

Recall:

Given:

m∠UXY = 58°

Since X is the midpoint of UV and Y is the midpoint of UW, therefore:

∠UXY and ∠V are corresponding angles.

m∠V = 58°

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m∠V = 58°

Solution:

Given data:

X is the midpoint of UV and Y is the midpoint of UW.

XY is parallel to VW.

Now, XY and VW are parallel lines cut by a transversal UV.

∠UXY and ∠UVW are corresponding angles.

If two parallel lines cut by a transversal, then the corresponding angles are congruent.

∠UXY ≅ ∠UVW

m∠UXY = m∠UVW

58 ° = m∠UVW

Switch the sides.

m∠UVW = 58°

⇒ m∠V = 58°

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step-by-step explanation: